supplementary line

Meaning

1. 1nouncountablemathematics

   An extra line drawn on a diagram to reveal relationships and help prove a theorem or solve a geometry problem.

   Grammar: Countable: draw a supplementary line, two supplementary lines. Also called an auxiliary line.

   Patterns

   • draw a supplementary line
   • add a supplementary line to a figure

   To prove the triangle theorem, the teacher drew a supplementary line parallel to the base.

   The problem became easy after she added a supplementary line through the center.

   A supplementary line is not part of the original figure but makes the proof clearer.

Word forms

Common combinations

draw a supplementary line

Draw a supplementary line from point A to point C.

add a supplementary line

You may need to add a supplementary line to see the angles.

dashed supplementary line

The dashed supplementary line showed where the figure could be split.

use a supplementary line

Many proofs use a supplementary line to build a helpful triangle.

Synonyms and how they differ

auxiliary line

Auxiliary line is the more common term in many textbooks and means exactly the same thing.

construction line

Construction line also describes a helping line in drawing, but in technical drawing it is often erased later and is not tied to proofs.

helper line

Helper line is informal and used in teaching, while supplementary line sounds more formal.

Word family

supplement noun

something added to complete or improve

supplementary adjective

added as an extra

supplementary angle noun

an angle that with another makes 180 degrees

supplementation noun

the act of adding something extra

Commonly confused: supplementary line or supplementary angles?

Practice

Make it your own

Write a sentence using “supplementary line”, then check it and compare it with the examples above.

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